The simplest trigonometric equations
Answers are for parents and teachers.
1
Solve 2 cos x + 1 = 0.
x = ± 2π/3 + 2πk, k ∈ ℤ
2
Solve sin 2x = 1/2.
x = (−1)ᵏ π/12 + πk/2, k ∈ ℤ
3
Solve tan x = √3.
x = π/3 + πk, k ∈ ℤ
4
Compute arcsin(√3/2) + arccos(1/2).
2π/3
5
Solve sin²x − 3 sin x + 2 = 0 and explain why one root is discarded.
Let sin x = t: t² − 3t + 2 = 0, t = 1 or t = 2. sin x = 2 is impossible; sin x = 1 gives x = π/2 + 2πk, k ∈ ℤ.